We propose a macroscopic approach toward realistic simulations of the population activity of hippocampal pyramidal neurons, based on the known refractory density equation with a different hazard function and on a different single-neuron threshold model. The threshold model is a conductance-based model taking into account adaptation-providing currents, which is reduced by omitting the fast sodium current and instead using an explicit threshold criterion for action potential events. Compared to the full pyramidal neuron model, the threshold model well approximates spike-time moments, postspike refractory states, and postsynaptic current integration. The dynamics of a neural population continuum are described by a set of one-dimensional partial differential equations in terms of the distributions of the refractory density (where the refractory state is defined by the time elapsed since the last action potential), the membrane potential, and the gating variables of the voltage-dependent channels, across the entire population. As the source term in the density equation, the probability density of firing, or hazard function, is derived from the Fokker-Planck (FP) equation, assuming that a single neuron is governed by a deterministic average-across-population input and a noise term. A self-similar solution of the FP equation in the subthreshold regime is obtained. Responses of the ensemble to stimulation by a current step and oscillating current are simulated and compared with individual neuron simulations. An example of interictal-like activity of a population of all-to-all connected excitatory neurons is presented.
The expected firing probability of a stochastic neuron is approximated by a function of the expected subthreshold membrane potential, for the case of colored noise. We propose this approximation in order to extend the recently proposed white noise model [A. V. Chizhov and L. J. Graham, Phys. Rev. E 75, 011924 (2007)] to the case of colored noise, applying a refractory density approach to conductance-based neurons. The uncoupled neurons of a single population receive a common input and are dispersed by the noise. Within the framework of the model the effect of noise is expressed by the so-called hazard function, which is the probability density for a single neuron to fire given the average membrane potential in the presence of a noise term. To derive the hazard function we solve the Kolmogorov-Fokker-Planck equation for a mean voltage-driven neuron fluctuating due to colored noisy current. We show that a sum of both a self-similar solution for the case of slow changing mean voltage and a frozen stationary solution for fast changing mean voltage gives a satisfactory approximation for the hazard function in the arbitrary case. We demonstrate the quantitative effect of a temporal correlation of noisy input on the neuron dynamics in the case of leaky integrate-and-fire and detailed conductance-based neurons in response to an injected current step.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with đź’™ for researchers
Part of the Research Solutions Family.